Average

To find the arithmetic mean , you need to add all the numbers and divide their sum by their number.

Example:

Find the arithmetic average of 2, 3 and 4.

Denote the arithmetic average by the letter m.

By definition, we find the sum of all numbers. 2 + 3 + 4 = 9.

Divide the resulting amount by the number of taken numbers. We have three numbers on condition.

As a result, we get the arithmetic mean formula :

What is the arithmetic mean for?

Besides the fact that he is constantly offered to be found in the lessons, finding the arithmetic mean is also very useful for saving time.

Example:

You can calculate how long your way from home to school (section, shop, etc.) takes. Considering that each time you spend different times on this path, you will not be able to accurately determine the time. Here the arithmetic mean comes to the rescue.

So, let you spend 25 minutes on the way on Monday, 29 minutes on Tuesday, 29 minutes on Wednesday, 20 minutes on Thursday, and 20 minutes on Thursday. Calculate the arithmetic average of the numbers:

In such a simple way, we got time, which we spend approximately on the way from home to school.

Average speed

The notion of average speed of motion is closely connected with the arithmetic mean.

Observing the traffic in the city, you can see that the cars accelerate and drive at high speed, they slow down and drive at low speed.

There are many such sections on the route of motor transport. Therefore, for convenience of calculations, use the concept of average speed.

Consider the average speed problem.

The task of the textbook "Vilenkin 5 class"

No. 1503

The car drove 3.2 hours along the highway at a speed of 90 km / h, then 1.5 hours along a dirt road at a speed of 45 km / h, finally 0.3 hours along a country road at a speed of 30 km / h. Find the average vehicle speed all the way.

To calculate the average speed of movement you need to know the entire path traveled by the car, and all the time that the car was moving.

S ₁ = V ₁ t ₁

S ₁ = 90 • 3.2 = 288 (km) - the highway.

S ₂ = V ₂ t ₂

S ₂ = 45 • 1.5 = 67.5 (km) - unpaved road.

S ₃ = V ₃ t ₃

S ₃ = 30 • 0.3 = 9 (km) - country road.

S = S ₁ + S ₂ + S ₃

S = 288 + 67.5 + 9 = 364.5 (km) - all the way traveled by car.

t = t ₁ + t ₂ + t ₃

t = 3.2 + 1.5 + 0.3 = 5 (h) - all the time.

V _cf = S: t

V _cf = 364.5: 5 = 72.9 (km / h) is the average vehicle speed.

Answer: V _cf = 72.9 (km / h) is the average vehicle speed.